Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | M16×D27 |
| Fitting | M16×C27 ⋊ C2 |
| Sylow | C27 ⋊ C2×M16 |
136 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | #100×D27, #13134250, #101×D27, … |
| maximal normal subgroup of | #100×D27, #13134250, #101×D27, … |
| maximal quotient of | #13134206, #13134207, #97×D27, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 122);